Physics Module for 2014 E.C.ESSLCE Exam

Vectors

• Scalar quantities: physical quantities with only magnitude, e.g., electric charge, density, mass
• Vector quantities: physical quantities with both magnitude and direction, e.g., velocity, force, torque, electric field

Vector Representation

• Analytical methods: represented by a letter with an arrow over its head or with bold face letter, e.g., →F or F, →P or P, →A or A
• Graphical/Geometrical methods: represented by a straight line with an arrow, where length is the magnitude and arrow direction is the direction

Vector Addition and Subtraction

• Resultant vector (R): the sum of two or more vectors
• Vector subtraction: addition of the negative vector, e.g., →R = →A - →B = →A + (-→B)
• Vector addition laws:
  • The resultant of two vectors with the same direction is the algebraic sum of the two vectors with the same direction as both.
  • Not commutative: order of vectors matters, e.g., →A + →B ≠ →B + →A
  • Associative: (→A + →B) + →C = →A + (→B + →C)

Key Concepts

• Magnitude: the size or amount of a vector
• Direction: the orientation or direction of a vectorHere are the study notes for the text:

Kinematics

• Definition: Kinematics is a branch of mechanics that describes the motion of an object without reference to the cause of motion (force).

One or Two Dimensional (2D) Motion

• Motion: Continuous change of position with time.
• Position: Location of an object with respect to a chosen reference frame or point.
• Reference Frame: A system of graduated lines symbolically attached to a body that serves to describe the position of points relative to the body.

Types of Motion

• Translational Motion: When all points of an object move the same distance in a given time.
  • Rectilinear motion: Object moves in a straight line (e.g. car moving in a straight line, bullet being fired).
  • Curvilinear motion: Object moves along a curved path (e.g. child going down a slide, bird flying in the sky).
• Rotational Motion: When an object moves about an axis and different parts of it move by different distances in a given interval of time.
  • Examples: Blades of a rotating fan, merry-go-round, blades of a windmill.
• Vibrational Motion: When a body moves to and fro about its mean position.
  • Examples: Pendulums, swings, tuning forks.

Let me know if this meets your requirements!### Vibrational Motion

• Vibrational motion can be periodic or non-periodic

Kinematics of the Particle

Motion in 1D

• Motion of a particle along a straight line in a fixed direction (or motion along one coordinate axis)
• Example: a car moving along a flat straight narrow road

Kinematical Terms

• Distance: total path length covered by the moving object
• Displacement: change of position (shortest distance between start and end of motion)
• Speed: rate of change of distance in a unit time
• Average Speed: total distance traveled by the total time required to cover the distance
• Velocity: rate of change of displacement as a function of time
• Average Velocity: change of displacement divided by the time interval during which the displacement occurs
• Instantaneous Velocity: velocity of the particle at a given instant of time (limit of average velocity as Δt approaches to zero)
• Instantaneous Speed: magnitude of instantaneous velocity

Acceleration

• Acceleration: rate of change of velocity
• Average Acceleration: change in velocity divided by the time interval during which the change in velocity occurs
• Instantaneous Acceleration: acceleration of the particle at a given instant of time (limit of average acceleration as Δt approaches to zero)

Uniform Motion in 1D

• Uniform Motion: equal distances traveled in equal intervals of time
• Acceleration: zero
• Velocity: remains constant
• Speed: equal to the actual speed
• Instantaneous Velocity: equal to the actual velocity

Uniformly Accelerated Motion in 1D

• Uniformly Accelerated Motion: motion with constant acceleration
• Velocity: changes with uniform rate
• Equations of Motion:
  • v(t) = vi + at
  • ∆x = vi t + (1/2) at^2
  • v^2 = vi^2 + 2a∆x

Free Falling Bodies

• Free Falling Bodies: objects moving freely under the influence of gravity alone
• Equations of Motion:
  • vy = gt
  • ∆y = (1/2) gt^2
  • vy^2 = 2g∆y

Two-Dimensional Motion

• Two-Dimensional Motion: motion in a plane (two coordinate axes simultaneously)
• Displacement: ∆~r = ~rB - ~rA
• Average Velocity: vav = ∆r / ∆t
• Instantaneous Velocity: v(t) = lim (∆~r / ∆t) as Δt approaches to zero
• Average Acceleration: aav = ∆v / ∆t
• Instantaneous Acceleration: a(t) = lim (∆~v / ∆t) as Δt approaches to zero

Projectile Motion

• Projectile Motion: motion of an object in a plane under the influence of gravity alone
• Trajectory: parabolic path
• Horizontal Motion: uniform motion (ax = 0)
• Vertical Motion: uniformly accelerated motion (ay = -g)
• Equations of Motion:
  • x(t) = v0x t
  • y(t) = v0y t - (1/2) gt^2
  • v0y = v0 sinθ
  • ymax = v0y^2 / 2g
  • t = 2v0y / g
  • R = v0^2 sin(2θ) / g

Circular Motion

• Circular Motion: motion in a circular path at a constant speed
• Uniform Circular Motion: constant speed and direction
• Velocity: not constant due to continuous change in direction
• Acceleration: radial acceleration (a = v^2 / r)